کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8900846 1631723 2018 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A modified primal-dual method with applications to some sparse recovery problems
ترجمه فارسی عنوان
یک روش اولیه دوبعدی اصلاح شده با برنامه های کاربردی برای برخی از مشکلات بازیابی جزئی
کلمات کلیدی
روش اولیه دوگانه، اپراتور نزدیکی، مشکلات بازیابی انعطاف پذیر،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی
In this paper, we first present a modified Chambolle-Pock primal-dual method (MCPPDM) to solve a convex composite optimization problem which minimizes the sum of two convex functions with one composed by a linear operator. It is well known that the Chambolle-Pock primal-dual method (CPPDM) with the combination parameter being 1 is an application of the proximal point algorithm and thus is convergent, however, when the combination parameter is not 1, the method may be not convergent. To choose flexibly the combination parameter, we develop a slightly modified version with little additional computation cost. In CPPDM, one variable is updated twice but another variable is updated only once at each iteration. However, in the modified version, two variables are respectively updated twice at each iteration. Another main task of this paper is that we reformulate some well-known sparse recovery problems as special cases of the convex composite optimization problem and then apply MCPPDM to address these sparse recovery problems. A large number of numerical experiments have demonstrated that the efficiency of the proposed method is generally comparable or superior to that of existing well-known methods such as the linearized alternating direction method of multipliers and the graph projection splitting algorithm in terms of solution quality and run time.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 333, 15 September 2018, Pages 76-94
نویسندگان
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